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I am working on a binary classification problem where one of the most interesting features has a distribution which looks more or less bimodal. Here is the distribution plot of that feature: enter image description here

The two modes seem to correspond to two classes. When I look at the distribution of this feature corresponding to each class separately, this is what I get: enter image description here

enter image description here

Clearly, one of them is more like a log-normal distribution, and the other is more like normal, and the two peaks in the original distribution seems to correspond to two different classes. My question is how do I deal with this kind of bimodality in Logistic regression. Also, would other machine learning algorithms be more suitable for this kind of a problem?

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    $\begingroup$ What does it mean to “deal with” the feature? Bimodality of the distribution isn’t an obstacle for logistic regression. $\endgroup$
    – Sycorax
    Commented Dec 17, 2021 at 20:25
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    $\begingroup$ The features in a logistic regression do not have distribution assumptions (except that constant features are unhelpful), so what problem do you see with your bimodal feature? $\endgroup$
    – Dave
    Commented Dec 17, 2021 at 20:29
  • $\begingroup$ If you know the two classes then you can incorporate them into your logistic regression $\endgroup$
    – Henry
    Commented Dec 17, 2021 at 20:50
  • $\begingroup$ @Henry I take that comment to mean that the two classes are the classes being predicted. $\endgroup$
    – Dave
    Commented Dec 17, 2021 at 20:55
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    $\begingroup$ @Dave you may be correct. I had guessed these were credit scores, that the two classes were something like "does not have a formal job" and "has a formal job" and the prediction was "will default" or "will not default" $\endgroup$
    – Henry
    Commented Dec 17, 2021 at 20:58

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Stick that feature in your regression like you would any other feature. Logistic regression makes no assumption that the features have a particular distribution. I suspect this misconception comes from the same confusion that people have about OLS linear regression.

Since the distribution of that feature for each $y$ category is not just a shift in location, you might benefit from using some nonlinear functions of this feature, such as a spline, but the distributions are so different that I expect this feature to give considerable discriminative ability on its own.

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